Monday, 26 June 2017

LOGARITHMS 2

 If log 3= 0.4771; find the value of log 90,000,000 without using tables.

solution

log90,000,000=log(10,000,000 x 9)

=log10,000,000 + log9

=log107 – log32

=7log10 – 2log3

=(7x1) –  2(0.4771)

=7– 0.9542

= 6.0458

Hence log 90,000,000 = 6.0458


TRY THIS……………


If log 3= 0.4771; find the value of log 270,000 without using tables.

FACTORIZE 1


Factorize 81-V2

Solution

We use difference of two squares a2 – b2 = (a - b)(a + b)

81-V2 = 92-V2       

        = (9 - V)(9 + V)

Hence 81 - V2 = (9 - V)(9 + V)


TRY THIS…………….



Factorize 64 - Z2

LOGARITHMS 1


If Logax = 41, find Loga(1/x2)

Solution

= Loga(1/x2)

= Logax-2

= -2 x Logax

= -2 x 41

= -82


TRY THIS………..
  

If Logab= 300, find Loga(1/b2)

FUNCTIONS 1

If F(x) = 8x + 10; Find F-1(42).


Solution


HINT: F-1(x) means inverse.

PROCEDURE:
Make x the subject and then interchange x and y variables.

Let y=F(x)

So,  y= 8x + 10

y – 10 = 8x

y – 10  = 8x
   8          8

y – 10   = x
   8

x  =   y – 10     after rearranging
           8

 y-1 = x – 10     after interchanging x and y variables.
             8

F-1(x) = x – 10     after interchanging x and y variables.
                8

Now we calculate F-1(42) as hereunder;

F-1(90) = 42 – 10     
                  8

F-1(90) =  32      
                8

F-1(90) =  4      [after dividing 32 by 8]
               
Hence, F-1(32) =  4   .      
                             


TRY THIS……………………………


If F(x) = 7x + 20; Find F-1(14).

MID-POINT 1


Find the midpoint of a line from (7, 14) to (17, 10)

Solution

x1=7, x2=17, y1=14, y2=10.

Mid point = (x1 + x2, y1 + y2)
                         2             2

Mid point = (7 + 17, 14 + 10)
                        2              2

Mid point = (24, 24)
                     2    2

Hence midpoint = (12, 12)

TRY THIS……………………..



Find the midpoint of a line from (16, 2) to (14, 16)

Friday, 26 May 2017

ACCOUNTS-2


From the following information you are required to prepare a balance sheet of BIBANJA & Co. LTD as at 06.09.2013
Creditors----------------------------120,000/=
Debtors ------------------------------250,000/=
Bank Overdraft---------------------80,000/=
Cash in Hand----------------------130,000/=
Stock------------------------------------57,000/=
Bank loan----------------------------200,000/=
Furniture------------------------------93,000/=
Premises-----------------------------260,000/=
Capital-------------------------------390,000/=

Solution

Balance sheet of BIBANJA & Co. LTD as at 06.09.2013

LIABILITIES
Amount
Amount
ASSETS
Amount
Amount

Capital

CURRENT LIABILITIES
Creditors
Bank Overdraft

LONG TERM LIABILITIES

Bank loan



 120,000
   80,000
390,000



200,000



200,000
FIXED  ASSETS
Premises
Furniture

CURRENT  ASSETS

Stock
Debtors
Cash in hand






  57,000
250,000
 130,000

260,000
  93,000





437,000


790,000


790,000



TRY THIS..................

From the following information you are required to prepare a balance sheet of MARUKU & Co. LTD as at 06.04.2015
Creditors----------------------------127,000/=
Debtors ------------------------------260,000/=
Bank Overdraft---------------------85,000/=
Cash in Hand----------------------140,000/=
Stock------------------------------------57,000/=
Bank loan----------------------------200,000/=
Furniture------------------------------93,000/=
Premises-----------------------------262,000/=

Capital-------------------------------400,000/=


LOGARITHMS 6



MIDPOINT-1

Find the midpoint of a line from (1, 14) to (17, 10)

Solution

x1=1, x2=17, y1=14, y2=10.

Mid point = (x1 + x2, y1 + y2)
                        2             2

Mid point = (1 + 17, 14 + 10)
                       2              2

Mid point = (18, 24)
                     2    2

Hence midpoint = (9, 12)

TRY THIS……………………..

  

Find the midpoint of a line from (6, 2) to (14, 6)

RADICALS 5



ALGEBRA 2


If │2x – 19 │= 21; Find  x

Solution

±(2x – 19 )= 21

2x -19= 21    OR   –(2x-19) = 21

2x – 19 = 21    OR   -2x+19= 21

2x = 21 + 19    OR   -2x= 21-19

2x = 40     OR   -2x  =  2
2      2                2        2

x = 20  OR  x = 1


Hence x = 20 OR x = 1     


TRY THIS...............................



If │4x – 12 │= 48; Find  x

LOGARITHMS 6



ANGLES 1


If x-70 and 4x + 220 are complementary angles, find the value of x.

Solution

Complementary angles add up to 900.

so,  x-70 + 4x + 220 = 900.
so,  x + 4x + 220 - 70 = 900.
so,  5x + 150 = 900.
so,  5x = 900 -  150
so,  5x = 750

so,  5x = 7515
      5      5

Hence x = 150

TRY THIS...............


If 3x - 40 and 7x + 540 are complementary angles, find the value of x.

NUMBER LINE 2



SETS 2


In Kasanga village the number of people who speak English or French is 300. 150 of them speak English and 170 of them speak French. How many speak both languages?

solution

In most cases, OR stands for union whereas AND/BOTH, stands for intersection.
Let French=n(F), English= n(E).

n(E)= 180,
n(F)= 170,
n(EuF) = 300,
n(EnF)=?


n(EuF) = n(E) + n(F) - n(EnF)

300  =  150 + 170 – n(EnF)

300  =  320 – n(EnF)

n(EnF) =  320 – 300

n(EnF) =  20

Hence n(EnF)=20 answer

  20 speak both languages   .


TRY THIS……..


In Malenda village the number of people who speak English or French is 280. 185 of them speak English and 175 of them speak French. How many speak both languages? 

RADICALS 4



EXPONENTIALS 4


Find x if 64x = 0.125; find x.

Solution

64x = 0.125
(26)x = 0.125          [since 64=26 ]
26x = 0.125          
26x = 125/1000     [converting 0.125 into fraction]       
26x = 1/8    [after simplifying]       
26x = 8-1           [since 1/a=a-1]
26x = (23)-1
26x = 23 x-1           
26x = 2-3           [since (ac)d =acd]
26x = 2-3           [same bases cancel out]
6x = -3         
6x = -3 -1        
6      6 2
x= -1/2
Hence x= -1/2  .

TRY THIS…………………….



Find x if 162m = 0. 5; find m.